RICHMOND — After a contentious legislative session that drew large protests and national ridicule to the state Capitol, Virginians are less supportive of Gov. Robert F. McDonnell and less optimistic about the direction of the state, according to a poll by The Washington Post.

The approval rating for McDonnell (R) dropped six points over the past year, from 62 percent to 56 percent. Thirty-five percent disapprove of the job he is doing — a nine-point increase from a year ago.

Suzanne Moore, a retired shop owner from Purcellville, said she was generally pleased with McDonnell’s performance except for his support of the ultrasound law, which she opposes.

“I believe in women’s rights,” said Moore, a 79-year-old independent voter. “I don’t see why they should have to jump through hoops that are put into law by the government that we’re being overrun by.”

Republicans hope McDonnell, an oft-mentioned vice presidential contender, will help deliver Virginia in November, when the state will play a crucial role in determining the outcome of the presidential race and the balance of power in the U.S. Senate. He has traveled the nation in support of presumptive GOP presidential candidate Mitt Romney and campaigned with him last week in Virginia.

As governor and head of the Republican Governors Association, McDonnell has developed a national following, appearing regularly on news programs and at GOP dinners. He began airing TV ads about his successes in Virginia and on Monday will start a tour of the state to highlight its low unemployment rate and top business rankings.

Fifty-two percent of women in Virginia approve of McDonnell’s job performance despite an 11 percentage point increase in his disapproval rating. Among independent women his disapproval jumped by 18 points.

More than seven in 10 independent voters, men and women, say that adding McDonnell to a national ticket would not affect their presidential choice — 8 percent are more likely to back Romney and 18 percent say it would push them toward President Obama.

Doug Murray, 70, an independent voter who said he probably would cast his ballot for Romney, said McDonnell spends too much time thinking about his next job.

“I think he’s a professional politician,” said Murray, who owns a real estate company in Roanoke. “He feels too much like the party line. I would like someone who has the backbone to say what he thinks.”

McDonnell, once among the most conservative voices in the legislature, has surprised his critics by working on kitchen-table issues such as jobs, schools and roads. He helped cut $4 billion from the state budget, paring spending to 2006 levels and not raising taxes.

Jose Moralo, an independent voter from Hampton, said he has been pleasantly surprised by McDonnell’s governing style.

“I think he’s done all right,” said Moralo, 51, who works in a youth ministry. “I think that he hasn’t been as extremist as I thought he was going to be.”

Virginians split on whether they were satisfied with policies taken up by the General Assembly this year — 49 percent have positive reactions and 43 percent do not, according to the poll.

State lawmakers considered several abortion-related measures during this year’s session, including one that bestowed rights on fertilized eggs and another that banned abortions after 20 weeks of a pregnancy. A majority of those polled — 59 percent — think abortion should be legal in all or most cases.

However, half of them oppose the ultrasound law. Democrats and independents are against the measure, and Republicans narrowly support it, the poll found. Men and women oppose it in nearly equal numbers.

Scott Hall, 41, a Republican from Loudoun County, said he has never voted for a Democrat and would like to see abortion outlawed. Yet he said he thinks Virginia is going in the wrong direction largely because of measures such as the ultrasound law. Hall said the legislation was more about “trying to create shame” than eliminating abortions.

“I do believe the law should support my position that abortion is wrong . . . but I want it to be based on science, not, ‘I’m going to show you a picture and you’re going to cry and you’re going to change your mind,’ ” said Hall, who sells network test equipment. “That’s not good law.”

McDonnell also signed a bill repealing the state’s one-per-month limit on handgun purchases. The cap was put in place 19 years ago, at a time when the state was a notorious supplier to gun traffickers along the East Coast.

Fifty-three percent in the poll support stricter gun-control laws. And 71 percent oppose the repeal of the limit, with solid majorities among Democrats, Republicans and independents.

State lawmakers also debated but eventually killed a popular measure that would have allowed home-schooled students to play sports at public high schools. But 64 percent of Virginians support the legislation, named for Tim Tebow, the NFL player who was home-schooled but was allowed to play football at a high school in Florida.

McDonnell’s lower approval rating and respondents’ view of state issues aside, Virginians approve of their U.S. senators.

Sen. Mark R. Warner (D) remains the most popular elected official in the commonwealth. A solid majority of Virginians — 63 percent — approve of the way he is handling his job. Twenty-six percent disapprove.

The popular former governor has seen his approval rating slide a bit since entering Congress — from 80 percent approval as governor in 2005, when he persuaded a GOP-led legislature to raise taxes for record investments in education, public safety and health care. He faces reelection in 2014.

Sen. James Webb (D) draws a 52 percent approval rating among Virginians. The one-term senator is not seeking reelection this year — paving the way for one of the most competitive Senate races nationally, probably between former governors George Allen (R) and Timothy M. Kaine (D).

The poll was conducted by telephone April 28 to May 2 among a random sample of 1,101 Virginia adults, including 964 registered voters and users of both conventional and cellular phones. Results from the full survey have a margin of sampling error of plus or minus 3.5 percentage points.

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